Considering the problem of how to efficiently transmit unknown quantum states in multi-unicast networks, we propose a nonlinear quantum network coding scheme with classical communication resource. On the conditions of free classical communication between adjacent nodes in a network, as well as unlimited capacities of classical channels, perfect quantum network coding is available. By means of local phase deviation correction, we design the encoding procedure of nonlinear coding scheme. Moreover, we provide the upper bound on the total number of classical communication which is required to achieve quantum communication, as well as the analysis of scheme property.